# CLEAN WORKSPACE AND LOAD PACKAGES --------------------------------------------
rm(list = ls())
library(datasim)
library(tidyverse)
# SIMULATE MULTIVARIATE SPATIAL DATA -------------------------------------------
# set.seed(4)
Corr <- matrix(c(1, -0.3, 0, -0.3, 1, 0.3, 0, 0.3, 1), nrow = 3)
sigmas <- rep(0.4^0.5, 3)
D <- diag(sigmas)
Cov <- D %*% Corr %*% D
# beta <- c(-0.5, 0, 0.5)
beta <- c(0, 0, 0)
variance <- 0.6 * matrix(c(1, 0, 0, 0, 1, 0, 0, 0, 1), nrow = 3)
cor.model <- "exp_cor"
cor.params <- list(list(phi = 0.05), list(phi = 0.05), list(phi = 0.1))
f <- list(
mean ~ mfe(x1, beta = get("beta")) +
mre(factor(id), sigma = get("Cov")) +
mgp(list(s1), variance = get("variance"), cor.model = get("cor.model"),
cor.params = get("cor.params"), range = 2),
sd ~ I(0)
)
n <- 300
m <- 3
(data_geo <- sim_model(formula = f, n = n, responses = m))
## # A tibble: 900 x 9
## id x1 s1 mre.factor.mean mgp.list.mean mean sd response
## <int> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 0.791 0.733 0.772 -0.311 0.461 0 0.461
## 2 2 0.659 1.53 -0.374 -0.432 -0.806 0 -0.806
## 3 3 -0.514 1.16 -0.697 -1.06 -1.75 0 -1.75
## 4 4 -0.826 1.34 0.285 -0.677 -0.392 0 -0.392
## 5 5 -1.05 1.01 0.522 0.135 0.657 0 0.657
## 6 6 -0.636 0.689 0.653 -0.267 0.386 0 0.386
## 7 7 -0.283 1.73 -0.0330 -0.806 -0.839 0 -0.839
## 8 8 -0.636 0.239 0.124 -0.363 -0.239 0 -0.239
## 9 9 0.141 0.964 0.113 -0.331 -0.218 0 -0.218
## 10 10 0.682 0.670 -0.432 0.0897 -0.342 0 -0.342
## # ... with 890 more rows, and 1 more variable: response_label <int>
# knitr::kable(head(data_model, 10))
# VISUALIZE MULTIVARIATE SPATIAL DATA ------------------------------------------
ggplot(data_geo, aes(x1, response)) +
geom_smooth(aes(col = factor(response_label))) +
geom_point(aes(col = factor(response_label)))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
ggplot(data_geo, aes(s1, mgp.list.mean)) +
geom_line(aes(col = factor(response_label)))
vg <- data_geo %>%
mutate(s2 = s1) %>%
group_by(response_label) %>%
nest() %>%
mutate(variog = purrr::map(data, ~ gstat::variogram(mgp.list.mean ~ 1, ~ s1 + s2, . ,
cutoff = 3, width = 0.005))) %>%
dplyr::select(-data) %>%
unnest()
ggplot(vg, aes(dist, gamma)) +
geom_point(aes(size = np)) +
geom_smooth() +
expand_limits(y = 0, x = 0) +
scale_x_continuous(limits = c(0, 3)) +
scale_y_continuous(limits = c(0, 1.3)) +
stat_function(fun = function(x) 0.6 * (1-exp(- x/0.05)), col = 2, size = 1) +
facet_wrap(~response_label, ncol = 1)
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## Warning: Removed 85 rows containing non-finite values (stat_smooth).
## Warning: Removed 85 rows containing missing values (geom_point).
vg <- data_geo %>%
mutate(s2 = s1) %>%
group_by(response_label) %>%
nest() %>%
mutate(variog = purrr::map(data, ~ gstat::variogram(response ~ 1, ~ s1 + s2, . ,
cutoff = 3, width = 0.005))) %>%
dplyr::select(-data) %>%
unnest()
ggplot(vg, aes(dist, gamma)) +
geom_point(aes(size = np)) +
geom_smooth() +
expand_limits(y = 0, x = 0) +
scale_x_continuous(limits = c(0, 3)) +
scale_y_continuous(limits = c(0, 2)) +
stat_function(fun = function(x) 0.4 + 0.6 * (1-exp(- x/0.05)), col = 2, size = 1) +
stat_function(fun = function(x) 0.4 + 0.6 * (1-exp(- x/0.1)), col = 3, size = 1) +
facet_wrap(~response_label, ncol = 1)
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## Warning: Removed 48 rows containing non-finite values (stat_smooth).
## Warning: Removed 48 rows containing missing values (geom_point).
# vg <- data_geo %>%
# mutate(s2 = s1) %>%
# dplyr::filter(response_label == 3) %>%
# gstat::variogram(mgp.list.mean ~ 1, ~ s1 + s2, . , cutoff = 3, width = 0.005)
# ggplot(vg, aes(dist, gamma)) +
# geom_point(aes(size = np)) +
# geom_smooth() +
# expand_limits(y = 0, x = 0) +
# scale_x_continuous(limits = c(0, 3)) +
# stat_function(fun = function(x) 0.6 * (1-exp(- x/0.05)), col = 2, size = 2)
data_geo %>%
dplyr::select(id, mre.factor.mean, response_label) %>%
spread(response_label, mre.factor.mean) %>%
dplyr::select(-id) %>%
GGally::ggpairs(aes(fill = "any"))
data_geo_wide <- data_geo %>%
dplyr::rename(ability = response, id_person = id) %>%
gather(var, value, mre.factor.mean:ability) %>%
mutate(var = paste0(var, response_label)) %>%
select(-response_label) %>%
spread(var, value)
# SIMULATE ITEM FACTOR DATA ----------------------------------------------------
q <- 10
init_data <- purrr::map(1:q, ~ data_geo_wide) %>%
purrr::reduce(rbind)
# n <- 300
difficulty <- matrix((1:q - 5)/10 * 2, nrow = 1)
discrimination1 <- seq(0.4, 1.5, length.out = q)
discrimination2 <- runif(q, 0, 2)
discrimination3 <- runif(q, 0, 2)
discrimination1[1] <- 1
discrimination1[c(3, 5, 8)] <- 0
discrimination2[1:2] <- c(0, 1)
discrimination2[c(4, 5, 10)] <- 0
# discrimination3[1:3] <- c(0, 0, 1)
# discrimination1 <- discrimination1 * 0.3
# discrimination2 <- discrimination2 * 0.3
cbind(discrimination1, discrimination2, discrimination3)
## discrimination1 discrimination2 discrimination3
## [1,] 1.0000000 0.000000 0.40052452
## [2,] 0.5222222 1.000000 1.10412733
## [3,] 0.0000000 1.098587 1.32626150
## [4,] 0.7666667 0.000000 1.57900160
## [5,] 0.0000000 0.000000 1.08222874
## [6,] 1.0111111 1.783167 1.32947141
## [7,] 1.1333333 1.505002 1.74563860
## [8,] 0.0000000 0.865549 0.05820813
## [9,] 1.3777778 0.300353 0.52441984
## [10,] 1.5000000 0.000000 0.70927425
f <- list(
prob ~ mfa(ones, beta = get("difficulty")) +
mfe(ability1, beta = get("discrimination1")) +
mfe(ability2, beta = get("discrimination2")),
# + mfe(ability3, beta = get("discrimination3")),
size ~ I(1)
)
data_long <- sim_model(formula = f,
link_inv = list(pnorm, identity),
generator = rbinom,
responses = q,
n = n,
init_data = init_data
)
data_long <- dplyr::rename(data_long, subject = id,
item = response_label, y = response)
# VISUALIZE ITEM FACTOR DATA ---------------------------------------------------
explor <- data_long %>%
group_by(subject) %>%
summarize(endorse = mean(y),
ability1 = unique(ability1),
ability2 = unique(ability2),
# ability3 = unique(ability3),
x1 = unique(x1))
ggplot(explor, aes(ability1, endorse)) + geom_point(alpha = 0.5)
ggplot(explor, aes(ability2, endorse)) + geom_point(alpha = 0.5)
# ggplot(explor, aes(ability3, endorse)) + geom_point(alpha = 0.5)
# ggplot(explor, aes(x1, endorse)) + geom_point(alpha = 0.5)
# PREPARE DATA -----------------------------------------------------------------
response <- data_long$y
coordinates <- dplyr::select(data_geo_wide, s1)
dist <- as.matrix(dist(coordinates))
# dist <- as.matrix(dist(dplyr::select(data_geo_wide, s1)[order(data_geo_wide$s1),]))
# dist <- dist[order(data_geo_wide$s1),]
n
## [1] 300
q
## [1] 10
m <- 2
iter <- 5 * 10 ^ 4
thin <- 5
# iter <- 5 * 10 ^ 3
cor.params <- c(0.04, 0.04)
sig.params <- c(0.6 ^ 0.5, 0.6 ^ 0.5)
fix.sigma <- 0.4^0.5
# sigma_prop <- matrix(c(0.138, -0.023, -0.023, 0.1), 2) * 2.38 ^ 2 / 2
sigma_prop <- 0.001 * diag(5)
disc_mat <- cbind(discrimination1, discrimination2)
L_a <- lower.tri(disc_mat, diag = TRUE) * 1
L_a[c(3,5,8), 1] <- 0
L_a[c(4,5,10), 2] <- 0
T_gp <- diag(m)
# diag(T_gp) <- 0
# T_gp[2,2] <- 0
# RUN --------------------------------------------------------------------------
Rcpp::sourceCpp("../src/mirt-gibss-sp.cpp")
source("../R/ggplot-mcmc.R")
Rcpp::sourceCpp("../src/ifa-driver.cpp")
source("../R/spmirt.R")
# # set.seed(5)
# system.time(
# samples <- ifa_gibbs_sp(response, dist, n, q, m, cor.params, sig.params,
# Corr[1:2, 1:2], fix.sigma, sigma_prop, L_a, T_gp, 0.234,
# iter)
# )
iter <- 5000
thin <- 5
system.time(
samples <- spmirt(
response = response, predictors = NULL, coordinates = coordinates,
standardize = TRUE,
nobs = n, nitems = q, nfactors = 2, niter = iter, thin = thin,
constrains = list(A = L_a, W = T_gp, V_sd = sigmas[1:2]/2),
adaptive = list(Sigma = NULL, Sigma_R = NULL, Sigma_gp_sd = NULL,
Sigma_gp_phi = NULL, scale = 1, C = 0.7, alpha = 0.8,
accep_prob = 0.234),
sigmas_gp_opt = list(initial = 0.6, prior_mean = 0.6, prior_sd = 0.4),
phi_gp_opt = list(initial = 0.05, prior_mean = 0.05, prior_sd = 0.4))
)
## Standardixing
## user system elapsed
## 437.705 305.496 205.306
iter = iter / thin
thin2 <- 1
attr(samples, "model_info")[-c(1, 2, 3)]
## $nobs
## [1] 300
##
## $nitems
## [1] 10
##
## $nfactors
## [1] 2
##
## $ngp
## [1] 2
##
## $niter
## [1] 5000
##
## $thin
## [1] 5
##
## $standardize
## [1] TRUE
##
## $constrain_L
## [,1] [,2]
## [1,] 1 0
## [2,] 1 1
## [3,] 0 1
## [4,] 1 0
## [5,] 0 0
## [6,] 1 1
## [7,] 1 1
## [8,] 0 1
## [9,] 1 1
## [10,] 1 0
##
## $constrain_T
## [,1] [,2]
## [1,] 1 0
## [2,] 0 1
##
## $constrain_V_sd
## [1] 0.3162278 0.3162278
##
## $adap_Sigma
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.001 0.000 0.000 0.000 0.000
## [2,] 0.000 0.001 0.000 0.000 0.000
## [3,] 0.000 0.000 0.001 0.000 0.000
## [4,] 0.000 0.000 0.000 0.001 0.000
## [5,] 0.000 0.000 0.000 0.000 0.001
##
## $adap_scale
## [1] 1
##
## $adap_C
## [1] 0.7
##
## $adap_alpha
## [1] 0.8
##
## $adap_accep_prob
## [1] 0.234
##
## $c_initial
## [1] 0.6984590 -0.8918420 -0.3100677 0.3747685 0.5509894 -0.1521639
## [7] -0.2630168 0.1391695 -0.4260893 -0.4334037
##
## $c_prior_mean
## [1] 0 0 0 0 0 0 0 0 0 0
##
## $c_prior_sd
## [1] 1 1 1 1 1 1 1 1 1 1
##
## $A_initial
## [,1] [,2]
## [1,] 1 0
## [2,] 0 1
## [3,] 0 0
## [4,] 0 0
## [5,] 0 0
## [6,] 0 0
## [7,] 0 0
## [8,] 0 0
## [9,] 0 0
## [10,] 0 0
##
## $A_prior_mean
## [,1] [,2]
## [1,] 1 0
## [2,] 0 1
## [3,] 0 0
## [4,] 0 0
## [5,] 0 0
## [6,] 0 0
## [7,] 0 0
## [8,] 0 0
## [9,] 0 0
## [10,] 0 0
##
## $A_prior_sd
## [,1] [,2]
## [1,] 0.45 1.00
## [2,] 1.00 0.45
## [3,] 1.00 1.00
## [4,] 1.00 1.00
## [5,] 1.00 1.00
## [6,] 1.00 1.00
## [7,] 1.00 1.00
## [8,] 1.00 1.00
## [9,] 1.00 1.00
## [10,] 1.00 1.00
##
## $R_initial
## [,1] [,2]
## [1,] 1 0
## [2,] 0 1
##
## $R_prior_eta
## [1] 1.5
##
## $B_initial
## [,1] [,2]
## [1,] NA NA
##
## $B_prior_mean
## [,1] [,2]
## [1,] NA NA
##
## $B_prior_sd
## [,1] [,2]
## [1,] NA NA
##
## $sigmas_gp_initial
## [1] 0.6 0.6
##
## $sigmas_gp_mean
## [1] 0.6 0.6
##
## $sigmas_gp_sd
## [1] 0.4 0.4
##
## $phi_gp_initial
## [1] 0.05 0.05
##
## $phi_gp_mean
## [1] 0.05 0.05
##
## $phi_gp_sd
## [1] 0.4 0.4
##
## $model_type
## [1] "spifa"
samples_tib <- as_tibble(samples, iter/2)
#summary(samples_tib)
samples_long <- gather(samples_tib)
as_tibble.spmirt.list(samples, 0, thin2, "c") %>%
gg_trace(alpha = 0.6)
as_tibble.spmirt.list(samples, 0, thin2, "a") %>%
gg_trace(alpha = 0.6)
as_tibble.spmirt.list(samples, iter/2, thin2, "a") %>%
gg_density(alpha = 0.5, ridges = TRUE, aes(fill = Parameters), scale = 4)
## Picking joint bandwidth of 0.122
as_tibble.spmirt.list(samples, iter/2, thin2, "theta") %>%
dplyr::select(1:100) %>%
gg_density(alpha = 0.5, ridges = TRUE, aes(fill = Parameters), scale = 4)
## Picking joint bandwidth of 0.13
as_tibble.spmirt.list(samples, 0, thin2, "theta") %>%
select(1:10) %>%
gg_trace(alpha = 0.6)
as_tibble.spmirt.list(samples, 0, thin2, "corr") %>%
gg_trace(alpha = 0.6)
as_tibble.spmirt.list(samples, 0, thin2, "mgp_sd") %>%
gg_trace(alpha = 0.6)
as_tibble.spmirt.list(samples, iter/2, thin2, "mgp_sd") %>%
gg_density(alpha = 0.5, ridges = FALSE, aes(fill = Parameters), scale = 4) +
stat_function(fun = dlnorm, colour = "red",
args = list(meanlog = log(0.6), sdlog = 0.4))
## Warning: Ignoring unknown parameters: scale
as_tibble.spmirt.list(samples, 0, thin2, "mgp_phi") %>%
gg_trace(alpha = 0.6)
as_tibble.spmirt.list(samples, iter/2, thin2, "mgp_phi") %>%
gg_density(alpha = 0.5, ridges = FALSE, aes(fill = Parameters), scale = 4) +
stat_function(fun = dlnorm, colour = "red",
args = list(meanlog = log(0.05), sdlog = 0.4))
## Warning: Ignoring unknown parameters: scale
as_tibble.spmirt.list(samples, 0, thin2, "a") %>%
gg_density2d(`Discrimination 1`, `Discrimination 2`, each = 10,
keys = c("Item ", "Discrimination "),
highlight = c(discrimination1, discrimination2))
## Warning: Computation failed in `stat_density2d()`:
## bandwidths must be strictly positive
## Warning: Computation failed in `stat_density2d()`:
## bandwidths must be strictly positive
## Warning: Computation failed in `stat_density2d()`:
## bandwidths must be strictly positive
## Warning: Computation failed in `stat_density2d()`:
## bandwidths must be strictly positive
## Warning: Computation failed in `stat_density2d()`:
## bandwidths must be strictly positive
## Warning: Computation failed in `stat_density2d()`:
## bandwidths must be strictly positive
as_tibble.spmirt.list(samples, 0, thin2, "a") %>%
gg_scatter(`Discrimination 1`, `Discrimination 2`, each = 10,
keys = c("Item ", "Discrimination "),
highlight = c(discrimination1, discrimination2))
as_tibble.spmirt.list(samples, iter/ 2, select = "a") %>%
summary() %>%
mutate(param = c(discrimination1, discrimination2)) %>%
gg_errorbarh() +
geom_point(aes(param, Parameters), col = 3)
as_tibble.spmirt.list(samples, iter/2, select = "c") %>%
summary() %>%
mutate(param = as.numeric(difficulty)) %>%
gg_errorbarh() +
geom_point(aes(param, Parameters), col = 3)
as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
dplyr::select(1:300) %>%
summary() %>%
mutate(param = data_geo$response[1:300]) %>%
gg_errorbarh(sorted = TRUE) +
geom_point(aes(x = param), col = 3)
as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
dplyr::select(301:600) %>%
summary() %>%
mutate(param = data_geo$response[301:600]) %>%
gg_errorbarh(sorted = TRUE) +
geom_point(aes(x = param), col = 3)
ability1_pred <- as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
dplyr::select(1:300) %>%
summary() %>%
mutate(param = data_geo$response[1:300],
s1 = data_geo$s1[1:300],
s2 = s1,
estim = `50%`)
ability1_pred %>%
ggplot(aes(s1, `50%`)) +
geom_line() +
geom_line(aes(s1, param, col = "real"))
vg <- gstat::variogram(estim ~ 1, ~ s1 + s2, ability1_pred, cutoff = 3, width = 0.01)
ggplot(vg, aes(dist, gamma)) +
geom_point(aes(size = np)) +
geom_smooth() +
expand_limits(y = 0, x = 0) +
scale_x_continuous(limits = c(0, 3))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
ability1_pred <- as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
dplyr::select(1:300)
ability1_pred <- ability1_pred[nrow(ability1_pred),]
ability1_pred <- ability1_pred %>%
summary.spmirt() %>%
mutate(param = data_geo$response[1:300],
s1 = data_geo$s1[1:300],
s2 = s1,
estim = `50%`)
ability1_pred %>%
ggplot(aes(s1, `50%`)) +
geom_line() +
geom_line(aes(s1, param, col = "real"))
vg <- gstat::variogram(estim ~ 1, ~ s1 + s2, ability1_pred, cutoff = 3, width = 0.01)
ggplot(vg, aes(dist, gamma)) +
geom_point(aes(size = np)) +
geom_smooth() +
expand_limits(y = 0, x = 0) +
scale_x_continuous(limits = c(0, 3))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
ability2_pred <- as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
dplyr::select(301:600) %>%
summary() %>%
mutate(param = data_geo$response[301:600],
s1 = data_geo$s1[301:600],
s2 = s1,
estim = `50%`)
ability2_pred %>%
ggplot(aes(s1, `50%`)) +
geom_line() +
geom_line(aes(s1, param, col = "real"))
vg <- gstat::variogram(estim ~ 1, ~ s1 + s2, ability2_pred, cutoff = 3, width = 0.005)
ggplot(vg, aes(dist, gamma)) +
geom_point(aes(size = np)) +
geom_smooth() +
expand_limits(y = 0, x = 0) +
scale_x_continuous(limits = c(0, 2))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## Warning: Removed 160 rows containing non-finite values (stat_smooth).
## Warning: Removed 160 rows containing missing values (geom_point).
ability2_pred <- as_tibble.spmirt.list(samples, iter/2, select = "theta") %>%
dplyr::select(301:600)
ability2_pred <- ability2_pred[nrow(ability2_pred),]
ability2_pred <- ability2_pred %>%
summary.spmirt() %>%
mutate(param = data_geo$response[301:600],
s1 = data_geo$s1[301:600],
s2 = s1,
estim = `50%`)
ability2_pred %>%
ggplot(aes(s1, `50%`)) +
geom_line() +
geom_line(aes(s1, param, col = "real"))
vg <- gstat::variogram(estim ~ 1, ~ s1 + s2, ability2_pred, cutoff = 3, width = 0.005)
ggplot(vg, aes(dist, gamma)) +
geom_point(aes(size = np)) +
geom_smooth() +
expand_limits(y = 0, x = 0) +
scale_x_continuous(limits = c(0, 2))
## `geom_smooth()` using method = 'loess' and formula 'y ~ x'
## Warning: Removed 160 rows containing non-finite values (stat_smooth).
## Warning: Removed 160 rows containing missing values (geom_point).
# # # PREPARE DATA FOR MODELLING ---------------------------------------------------
# #
# # Y <- data_model %>% dplyr::select(id, response, response_label) %>%
# # spread(response_label, response) %>%
# # arrange(id) %>%
# # dplyr::select(-id) %>%
# # as.matrix()
# #
# # X <- data_model %>% dplyr::select(id, matches("^x[[:digit:]]+$")) %>%
# # unique() %>%
# # arrange(id) %>%
# # dplyr::select(-id) %>%
# # as.matrix()
# #
# # Beta <- matrix(beta, nrow = 1)
# # Sigma_proposal <- diag(1, 3)
# #
# # # RUN MODEL --------------------------------------------------------------------
# #
# # getwd()
# # Rcpp::sourceCpp("../src/multi-lm.cpp")
# # source("../R/ggplot-mcmc.R")
# #
# # iter <- 10^6
# # system.time(
# # samples <- multi_lm(Y, X, iter, 0.01 * Sigma_proposal, 0.001 * Sigma_proposal)
# # )
# # samples %>% map(~ tail(.))
# #
# # # apply(samples$beta, 2, mean)
# # # cor(samples$beta)
# #
# # # Visualize traces
# # as_tibble(samples, 0, 100, select = "beta") %>%
# # gg_trace(wrap = TRUE, alpha = 0.6)
# #
# # as_tibble(samples, 0, 100, select = "beta") %>% gg_trace(alpha = 0.6)
# # as_tibble(samples, 0, 100, select = "corr_chol") %>% gg_trace(alpha = 0.6)
# # as_tibble(samples, 0, 100, select = "corr") %>% gg_trace(alpha = 0.6)
# # as_tibble(samples, 0, 100, select = "sigmas") %>% gg_trace(alpha = 0.6)
# #
# # bla <- as_tibble(samples, iter/2, select = "sigmas")
# # cov(log(bla))
# # nrow(unique(bla)) / nrow(bla)
# #
# # bla <- as_tibble(samples, iter/2, select = "corr_chol")
# # cov(bla)
# # nrow(unique(bla)) / nrow(bla)
# #
# # # Visualize densities
# #
# # as_tibble(samples, iter / 2, select = "corr_chol") %>%
# # gg_density(aes(fill = Parameters), scale = 2, alpha = 0.5, ridges = TRUE)
# #
# # as_tibble(samples, iter / 2, select = "corr") %>%
# # gg_density(aes(fill = Parameters), scale = 1, alpha = 0.5, ridges = TRUE)
# #
# # # Visualize credible intervals
# # as_tibble(samples, iter / 2, select = "beta") %>%
# # summary() %>%
# # mutate(param = beta) %>%
# # gg_errorbarh() +
# # geom_point(aes(param, Parameters), col = 3)
# #
# # Corr_chol <- t(chol(Corr))
# # corr_chol <- Corr_chol[lower.tri(Corr_chol, diag = TRUE)]
# # corr <- Corr[lower.tri(Corr)]
# #
# # as_tibble(samples, iter / 2, select = "corr_chol") %>%
# # summary() %>%
# # mutate(param = corr_chol) %>%
# # gg_errorbarh() +
# # geom_point(aes(param, Parameters), col = 3)
# #
# # as_tibble(samples, iter / 2, select = "corr") %>%
# # summary() %>%
# # mutate(param = corr) %>%
# # gg_errorbarh() +
# # geom_point(aes(param, Parameters), col = 3)
# #
# #
# # as_tibble(samples, iter / 2 ,select = "sigmas") %>%
# # summary() %>%
# # mutate(param = sigmas) %>%
# # gg_errorbarh() +
# # geom_point(aes(param, Parameters), col = 3)
# #
# #
# # # Visualize credible intervals for all Parameters
# # as_tibble(samples, iter / 2) %>%
# # summary() %>%
# # mutate(param = c(beta, corr_chol, corr, sigmas)) %>%
# # gg_errorbar() +
# # geom_point(aes(Parameters, param), col = 3)
# #